100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

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150 R. H. Priceform a hole. In terms of the proper time that describes the physics local tothe collapsing surface, passage through the event horizon is continuous andsmooth.II. Observing the unobservable black holeNo information can propagate outward through the event horizon, butthe compactness of a black hole means that the gravitational influence ofthe hole on its near environment gives rise to exotic phenomena (bendingof light rays, generation of X-rays, gravitational waves. . . ).III. Newtonian-like points, or spacetime regionsIt is a matter of distance from the hole. In a study of the properties ofspacetime very near a black hole, the focus is on the defining properties, thenonsingular one-way nature of the event horizon. At distances several timesr g , however, the main influence of the hole is its 1/r 2 pull. It therefore actson its environment like a Newtonian gravitational source and simple argumentsabout relative frames and momentum conservation at large distancesshow that the hole must move like a Newtonian object.IV. Black holes: simple or exceedingly unsimpleThe stationary Schwarzschild and Kerr spacetimes are very clean andsimple. Dynamical black holes are sufficiently complicated that an understandingof them can come only through numerical relativity, and thatunderstanding is still some time in the future.The history of the black hole has very much paralelled the place ofEinstein’s theory in science. The Schwarzschild geometry dates to the verystart of general relativity. There was limited interest in general relativity,and limited understanding of black holes among most astronomers until theearly 60s. New astronomical discoveries, starting with quasars, opened thepossibility that Einstein’s theory had an astrophysical role beyond cosmology.Now, almost a half century later, the transition is complete. It is nowall but taken for granted that supermassive black holes lie at the centers ofmany, perhaps all, galaxies, and that certain point-like X-ray sources areevidence of stellar mass holes.AcknowledgmentsThis work was supported by National Science Foundation grantPHY0244605, and NASA grant ATP03-0001-0027. I thank Frederick Jenetfor useful comments on the manuscript.
The Physical Basis of Black Hole Astrophysics 151References1. J. B. Hartle, Gravity: An Introduction to Einstein’s General Relativity (AddisonWesley, San Francisco, 2003).2. S. Carroll, Spacetime and Geometry: An Introduction to General Relativity(Addison Wesley, San Francisco, 2004).3. K. Schwarzschild, Sitzber. Deut. Akad. Wiss. Berlin, Kl. Math.-Phys. Tech.189, (1916).4. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (Freeman, SanFrancisco, 1973), Sec. 31.4.5. B. Carter, Phys. Rev. 174, 1559 (19968).6. J. A. Wheeler, Phys. Rev. 97,511 (1955).7. K. D. Kokkotas and B. G. Schmidt, Living Rev. Rel. 2, 2(1999): cited onMarch 26, 2005.8. R. D. Blandford and R. L. Znajek, Mon. Not. Roy. Astron. Soc. 179, 433(1977).9. Black Holes:The Membrane Paradigm, edited by K. S. Thorne, R. H. Price,and D. A. Macdonald (Yale University Press, London, 1986).10. D. P. Bennett et al., American Astronomical Society, 195th AAS Meeting,#37.07; Bulletin of the American Astronomical Society, 31, 1422 (1999).11. C. M. Miller, Astrophys. J., 618, 426 (2005).12. M. A. Abramowicz ed. it Theory of Black Hole Accretion Discs (CambridgeUniversity Press, Cambridge, 1998).13. J. H. Krolik Active Galactic Nuclei (Princeton University Press, Princeton,1998)14. Ribó, M. and Paredes, J. M. and Martí, J. and Casares, J. and Bloom, J. S.and Falco, E. E. and Ros, E. and Massi, M., “Results of a search for newmicroquasars in the Galaxy,” Revista Mexicana de Astronomia y AstrofisicaConference Series, Revista Mexicana de Astronomia y Astrofisica ConferenceSeries, 23 (2004).15. S. Rowan and J. Hough, “Gravitational Wave Detection by Interferometry(Ground and Space),” Living Rev. Relativity 2, (2000), 3. [Online article]:cited on 28 March, 2005, http://relativity.livingreviews.org/Articles/lrr-2000-3/index.html16. E. Poisson, Living Rev. Relativity, 7, 6 (2004).17. M. Sasaki and H. Tagoshi, ”Analytic Black Hole Perturbation Approach toGravitational Radiation”, Living Reviews in Relativity, 6, 6 (2003).
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Published byWorld Scientific Publis
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viA. Ashtekarof space-time that eme
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viiiA. AshtekarGravitational waves
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xviContents9. Receiving Gravitation
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4 J. Stachel(2) the change over tim
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6 J. StachelFig. 2respectively. Fur
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8 J. Stachelof string theory, M-the
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10 J. StachelLogically, it would se
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12 J. Stachelupon by no (net) exter
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14 J. Stachelof the incompatibility
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16 J. Stachelis an important differ
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18 J. Stachelbetween physical conce
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20 J. Stachel10. Four-Dimensional F
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22 J. Stachelderivative of the metr
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24 J. Stachel(b) General relativity
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26 J. Stachelfour-dimensional analo
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28 J. Stachelply the lessons learne
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30 J. Stachelmanifold appropriate f
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32 J. Stachelwhich merely defines t
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34 J. Stacheldynamical process as a
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36 J. Stachel9. J. Stachel, Special
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Part IIEinstein’s UniverseRamific
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40 H. Nicolai• Higher dimensions
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42 H. Nicolaiadvance, and possibly
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44 H. NicolaiBianchi identities are
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46 H. NicolaiIt does not appear pos
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48 H. NicolaiThe other SL(2, R), of
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50 H. Nicolai3.1. BKL dynamics and
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52 H. Nicolaidegrees of freedom, th
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54 H. Nicolaiin the valley. The Ham
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56 H. NicolaiThe main feature of th
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58 H. Nicolai4. Basics of Kac Moody
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60 H. Nicolaifor indefinite A. It i
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62 H. NicolaiThe level l = 0 sector
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64 H. NicolaiConsequently, the repr
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66 H. Nicolaiwhere the abelian part
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68 H. Nicolaiconstant momenta Π yi
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70 H. Nicolaiσ-model side is suppo
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72 H. NicolaiReferences1. H.A. Buch
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74 H. Nicolai44. G. Neugebauer and
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CHAPTER 3THE NATURE OF SPACETIME SI
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78 A. D. Rendallspacetime to define
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80 A. D. RendallOne of the most imp
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82 A. D. Rendalltheorems was an elu
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84 A. D. Rendallsymmetric solution
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86 A. D. Rendallback into a curvatu
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88 A. D. Rendallspace and there are
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The Nature of Spacetime Singulariti
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CHAPTER 4BLACK HOLES - AN INTRODUCT
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Black Holes 95It follows that ˙v d
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Black Holes 973221100-1-1-2-200-5-3
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Page 193 and 194: CHAPTER 7UNDERSTANDING OUR UNIVERSE
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Understanding Our Universe: Current
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Understanding Our Universe: Current
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CHAPTER 8WAS EINSTEIN RIGHT? TESTIN
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Was Einstein Right? 207We begin in
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Was Einstein Right? 20910 -810 -9E
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Was Einstein Right? 211On this 100t
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Was Einstein Right? 213The SME and
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Was Einstein Right? 215where d is t
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Was Einstein Right? 217of VLBI data
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Was Einstein Right? 219milliarcseco
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Was Einstein Right? 2215. Gravitati
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Was Einstein Right? 223be measured
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Was Einstein Right? 22510. J. G. Wi
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Was Einstein Right? 22761. C. M. Wi
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Receiving Gravitational Waves 229th
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Receiving Gravitational Waves 231gr
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Receiving Gravitational Waves 233Th
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Receiving Gravitational Waves 235We
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Receiving Gravitational Waves 23719
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Receiving Gravitational Waves 239th
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Receiving Gravitational Waves 241to
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Receiving Gravitational Waves 243In
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Receiving Gravitational Waves 245
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Receiving Gravitational Waves 247a
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Receiving Gravitational Waves 249ab
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Receiving Gravitational Waves 251Fi
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Receiving Gravitational Waves 253Eq
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Receiving Gravitational Waves 255In
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CHAPTER 10RELATIVITY IN THE GLOBAL
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Relativity in the Global Positionin
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Part IIIBeyond EinsteinUnifying Gen
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CHAPTER 11SPACETIME IN SEMICLASSICA
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Spacetime in Semiclassical Gravity
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CHAPTER 12SPACE TIME IN STRING THEO
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Space Time in String Theory 313limi
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Space Time in String Theory 315luti
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Space Time in String Theory 317In s
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Space Time in String Theory 319of t
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Space Time in String Theory 321an o
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Space Time in String Theory 323arbi
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Space Time in String Theory 325an e
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Space Time in String Theory 327in a
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Space Time in String Theory 329doma
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Space Time in String Theory 331a tu
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Space Time in String Theory 333bran
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Space Time in String Theory 335is a
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Space Time in String Theory 337thes
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Space Time in String Theory 339The
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Space Time in String Theory 341gene
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Space Time in String Theory 343are
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Space Time in String Theory 345tion
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Space Time in String Theory 34723.
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Space Time in String Theory 34955.
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Gravity, Geometry and the Quantum 3
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£¢¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
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Loop Quantum Cosmology 383inflation
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Loop Quantum Cosmology 385gravitati
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Loop Quantum Cosmology 387Secondly,
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Loop Quantum Cosmology 389sically d
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Loop Quantum Cosmology 391states an
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Loop Quantum Cosmology 393represent
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Loop Quantum Cosmology 3954.2.1. Di
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Loop Quantum Cosmology 397question
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Loop Quantum Cosmology 399exist. Th
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Loop Quantum Cosmology 401in the ex
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Loop Quantum Cosmology 403λ max or
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Loop Quantum Cosmology 405This happ
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Loop Quantum Cosmology 407Loop quan
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Loop Quantum Cosmology 409to obtain
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Loop Quantum Cosmology 411familiar
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Loop Quantum Cosmology 41334. M. Bo
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CHAPTER 15CONSISTENT DISCRETE SPACE
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Consistent Discrete Space-Time 417v
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Consistent Discrete Space-Time 419I
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Consistent Discrete Space-Time 421a
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Consistent Discrete Space-Time 423F
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Consistent Discrete Space-Time 4250
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Consistent Discrete Space-Time 4272
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Consistent Discrete Space-Time 429i
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Consistent Discrete Space-Time 431a
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Consistent Discrete Space-Time 433n
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Consistent Discrete Space-Time 435t
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Consistent Discrete Space-Time 437w
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Consistent Discrete Space-Time 439f
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Consistent Discrete Space-Time 441(
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Consistent Discrete Space-Time 443R
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CHAPTER 16CAUSAL SETS ANDTHE DEEP S
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Causal Sets and the Deep Structure
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CHAPTER 17THE TWISTOR APPROACH TOSP
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The Twistor Approach to Space-Time
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INDEXσ models, 57, 65, 693+1 formu
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Index 509inflation, 383, 385-387, 4
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